Leakage-Resilient Spatial Encryption

Spatial encryption is a generic public-key cryptosystem where vectors play the role of public keys and secret keys are associated to affine spaces. Any secret key associated to a space can decrypt all ciphertexts encrypted for vectors in that space, and the delegation relation is defined by subspace inclusion. Though several constructions of spatial encryption schemes have been proposed in the literature, none of them are known to remain secure in the leakage-resilient setting, in which the adversary may be capable of learning limited additional information about the master secret key and other secret keys in the system. In this paper, we propose the first spatial encryption scheme achieving leakage resilience in the standard model, based on existing static assumptions over bilinear groups of composite order. Our new scheme is based on the leakageresilient HIBE scheme by Lewko, Rouselakis, and Waters in TCC 2011 and can be seen as a generalization of Moriyama-Doi spatial encryption scheme to the leakage-resilient setting.